GCF of 7728/345, 7714/9300
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7728/345, 7714/9300 i.e 14/213900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7728/345, 7714/9300.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 7728/345,7714/9300?
Given fractions are 7728/345,7714/9300
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 7728/345,7714/9300, numerators are 7728,7714
Denominators are 345,9300
The GCF of 7728,7714 is 14 .
LCM of 345,9300 is 213900.
The greatest common factor of 7728/345,7714/9300 = [GCF of 7728,7714]/[LCM of 345,9300]= 14/213900
Therefore, the GCF of 7728/345,7714/9300 is 14/213900.
To find the highest common factor of 7728,7714, we have to find the factors of both numbers and list the highest common factor.
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The factors of 7714 are 1, 2, 7, 14, 19, 29, 38, 58, 133, 203, 266, 406, 551, 1102, 3857, 7714
The HCF of 7728,7714 is 14.
Lets's calculate GCF of 7728,7714
| 2 | 7728, 7714 |
| 7 | 3864, 3857 |
| 552, 551 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 7728,7714 By Matching Biggest Common Factor Method
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Now, list down the factors of 7714
:1,2,7,14,19,29,38,58,133,203,266,406,551,1102,3857,7714
Greatest Common Factor
We found the factors 7728,7714 . The biggest common factor number is the GCF number.
So the greatest common factor 7728,7714 is 14.
Lets's calculate LCM of 345,9300
| 3 | 345, 9300 |
| 5 | 115, 3100 |
| 23, 620 |
∴ So the LCM of the given numbers is 3 x 5 x 23 x 620 = 213900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/213900
Therefore, the GCF of Fractions 7728/345,7714/9300 is 14/213900
Least Common Multiple of 345,9300 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 345,9300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(345,9300) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(345,9300) x common factors =15 x 1 = 15
LCM(345,9300) = ( 345 × 9300 ) / 15
LCM(345,9300) = 3208500 / 15
LCM(345,9300) = 213900
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 7728/345, 7714/9300
1. What is the HCF of 7728,7714?
The HCF of 7728,7714 is 14
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 7728/345, 7714/9300?
Answer: GCF of Numerators as per given numbers 7728/345, 7714/9300 is
GCF of Numerators i.e. for 7728,7714 is 14
LCM of denominators i.e. for 345,9300 is 213900.
Thus, GCF of Fractions is 14/213900.Finally, GCF of Fractions for 7728/345, 7714/9300 is 14/213900.